C₅²×C₁₉×Dic₇ #27210872

order	13300
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₄×C₅²×C₁₉ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅²×C₁₉×Dic₇
unambiguous semidirect product	C₇⋊(C₄×C₅²×C₁₉)

96 conjugacy classes of subgroups.

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 13300

A minimal faithful permutation representation — 2 generators on 40 points:

(2,3)(4,5)(6,7)(8,11,10,9)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30)(36,37,38,39,40);(1,2,4,6,7,5,3)(31,32,33,34,35)

4750 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13300, 30);